A Chebyshev method for the numerical solution of the one-dimensional heat equation

Abstract

Chebyshev series can be used not only for representing explicit functions but also for solving differential equations. Two Chebyshev methods, the selected points method and the tau method, have been described by Lanczos2 for the solution of ordinary differential equations. Moreover both methods have applications to partial differential equations. In a previous paper1 we have applied the selected points technique to derive a two-dimensional Chebyshev method for the solution of partial differential equations over bounded regions. And in the present paper we generalize the tau method to provide a one-dimensional method for the solution of the heat conduction equation over an infinite strip.